Răspuns:
E(x) =(2x+3)² - (2x -1)(4-x) -2 (x+2)²+3x-2
a) E(x) = 4x²+2*2x*3+3²-(8x-2x²-4+x) -2*(x²+4x+4)+3x-2
E(x)=4x²+12x+9-9x+2x²+4-2x²-8x-8+3x-2
E(x) = 4x²-2x+3
b) E(n) =4n²-2n+3
E(n) ≥2(n+4)+3
4n²-2n+3≥2n+8+3
4n²-2n+3≥2n+11
4n²-2n-2n≥11-3
4n²-4n≥8
4n²-4n-8 ≥0 | :4
n²-n-2 ≥0
a= 1 ,b= -1 ,c= -2
Δ=b²-4ac =(-1)²-4*1*(-2) =1+8 =9
n1 = (-b+√Δ)/2a =( -(-1) +√9)/2 *1 = (1+3)/2 =4/2 =2
n2 = (-b-√Δ)/2a =( -(-1) -√9)/2 *1 = (1-3)/2 = -2/2 = -1
S;( -1;2)
Explicație pas cu pas:
